When Suzanne Kail, an English teacher at a public high school in Magnolia, Ohio, was told that she would be required to teach her students Latin and Greek word roots, she groaned and rolled her eyes. Kail believes in a progressive approach to education, in which active engagement in meaningful learning is paramount. In an account of her experience in the English Journal, she wrote, “asking students to do rote memorization was the antithesis of what I believed in most.” Still, her department head insisted on it, so Kail went forward with the attitude, “I’ll do it, but I won’t like it.” She was sure her students wouldn’t like it, either.

Kail was in for a surprise — as is anyone who takes a look at a raft of recent studies supporting the effectiveness of “old school” methods like memorizing math facts, reading aloud, practicing handwriting and teaching argumentation (activities that once went by the names drill, recitation, penmanship and rhetoric). While the education world is all abuzz about so-called 21st century skills like collaboration, problem solving and critical thinking, this research suggests that we might do well to add a strong dose of the 19th century to our children’s schooling.

Kail’s experience is instructive. As soon as she began teaching her students the Greek and Latin origins of many English terms — that the root sta means “put in place or stand,” for example, and that cess means “to move or withdraw” — they eagerly began identifying familiar words that incorporated the roots, like statue and recess. Her three classes competed against one another to come up with the longest list of words derived from the roots they were learning. Kail’s students started using these terms in their writing, and many of them told her that their study of word roots helped them answer questions on the SAT and on Ohio’s state graduation exam. (Research confirms that instruction in word roots allows students to learn new vocabulary and figure out the meaning of words in context more easily.) For her part, Kail reports that she no longer sees rote memorization as “inherently evil.” Although committing the word roots to memory was a necessary first step, she notes, “the key was taking that old-school method and encouraging students to use their knowledge to practice higher-level thinking skills.”

That’s also true of another old-fashioned method: drilling math facts, like the multiplication table. Although many progressive educators decry what they call “drill and kill” (kill students’ love of learning, that is), rapid mental retrieval of basic facts is a prerequisite for doing more complex, and more interesting, kinds of math. The only way to achieve this “automaticity,” so far as anyone has been able to determine, is to practice. And practice. Indeed, many experts who have observed the wide gap between the math scores of American and Chinese students on international tests attribute the Asian students’ advantage to their schools’ relentless focus on memorizing math facts. Failure to do so can effectively close off the higher realms of mathematics: a study published in the journal Mathematical Cognitionfound that most errors made by students working on complex math problems were due to a lack of automaticity in basic math facts.

Here are a few other old-school skills that are still worth cultivating:

HandwritingResearch shows that forming letters by hand, as opposed to typing them into a computer, not only helps young children develop their fine motor skills but also improves their ability to recognize letters — a capacity that, in turn, predicts reading ability at age 5. But many schools are now emphasizing typing over writing. Last year, for example, the Indiana Department of Education announced that the state’s public schools no longer had to teach cursive writing and they should ensure that students were “proficient in keyboard use” instead.

Argumentation
In a public sphere filled with vehemently expressed opinion, the ability to make a reasoned argument is more important than ever. Educational research on argumentation demonstrates that it helps students learn better too. A study published in the Journal of Research in Science Teaching in 2010, for example, found that 10th-graders who were taught how to construct an argument as part of their lessons on genetics not only had better arguments but also demonstrated a better understanding of the material.

Reading AloudMany studies have shown that when students are read to frequently by a teacher, their vocabulary and their grasp of syntax and sentence structure improves. Educator Doug Lemov, author of Teach like a Champion and a co-author of the new book Practice Perfect, explains why: “Children who are read to become familiar with the sound and rhythm and complexity of language long before they can produce it themselves. By virtue of being exposed to a wide variety of writing types and styles, they come to understand that the use of language involves intentional choices made by the author and is representative of the author’s time and place.”

Stories are especially powerful when narrated by a good reader, says Lemov, “someone who brings the story to life, models expressive reading and shows kids what a book ‘sounds like’ in the voice of someone who reads with passion.” But reading aloud, he adds, is a “dying art.” Maybe we adults should brush up on our old-school skills too.

Instant recall (automaticity) of relevant facts and nomenclature is an enabler of efficient higher-order thinking.

"Automaticity" is neither "Accuracy" (error free) nor "Fluency" (fast & error free). The key distinction being that automaticity by definition means "without noticeable demand on cognitive resources". The human brain can recall 7x7=49 when in the middle of an unfolding car crash. It cannot however recall what it had for breakfast in the middle of that same car crash (unless it chooses at its own peril to direct its conscious attention away from the moment at hand). For those who are interested in the neuroscience, consider reading up on the differences between hypocampal and neocortical memory.

Automaticity of fact recall is invaluable for anyone, student or expert alike, who wishes to engage their mind fully in higher-order thinking.

The debate should be focused on the method(s) of developing automaticity.

Methods of developing automaticity are legion. Some methods are more creative and some methods are more mechanistic. The core issue issue is not whether automaticity is a good thing. Instead, it is: what methods should we employ / not employ in order to develop automaticity of desired facts?

From the point of view of a homeschool Mom( with a certificate in home based education and a doctorate in theology, who has been educating her children at home for 10 years) rote memorization is the key to success. I don't understand how "well" educated people are missing this strong fact.

When a person memorizes the basics of any art may it be math, science, Latin, language arts or history or the million and one other studies out there, they are building a foundation for higher learning.

If a student learns the foundation they spend a lot less time trying to figure out the steps and concentrate on the theory.

A good indication that rote memorization is indeed the way, is to take a good look at our educational system that has been infiltrated by those who are in essence experimenting on our children in public schools.The last 25 years have been a failure,as seen by low test scores, as well as low IQ scores.Without the basics, these kids can't even think.

When I was in school, reading, writing and arithmetic (do you remember "The 3 R's?") were the core of education.

We learned these foundations so in higher grades we weren't trying to figure out each word, in every sentence.

The complete understanding came with time and maturity, as we expanded our realms of thinking and learning.

In our state, homeschooled kids are required to be tested every year. This year I decided to do a different test called the Terra Nova test. It's 5 hour test that consists of a great deal of critical thinking. My children (3 that are still at home) scored off the charts, literally. All 3 of them scored in the 12.9 grade level in many of the subjects. Rote memorization is so necessary that to argue against it is asinine.If the utter failure of the public school system isn't enough to convince you then you are part of the problem. Most of our early forefathers and scientific genius' were also homeschooled and practiced reading out loud daily , and their handwriting was beautiful. They make the so-called genius' of today look like kindergarteners. What I really want to know is, why is the educational system trying so hard to dumb our kids down?

Their "new" ways of learning are a sham,a thing that is not what it is purported to be, a failure, their intended objective is the opposite of success.

It's designed from the ground up to promote agriculture and is strictly intended to create a population that has some rudimentary skills at reading instructions and following directions and that's about it. It changed not at all when the Industrial Revolution altered the place of working from the field to the factory. The focus remained unchanged because the kind of worker that was needed remained unchanged.

It was never intended to provide any more than the basics to create good, little, mindless worker drones.

Unfortunately, while the essence of primary education remains the same, society has changed a good deal and the focus of a primary education needs to change. In an increasingly complex society, where employment is no longer a sure thing, or a life-time commitment to the same organization, people must learn how to think for themselves. That means they must be able to reason and think objectively and critically in order to get by.

Route memorization is pointless if there is no application or purpose to it. One must learn the WHY'S of things as well as the who, what, when, where and/or how's. Why's give motivation to learn the rest and teaches people to question things. That encourages critical thinking - a skill that must be started and nurtured early in people before the indoctrination of religion, prejudice and politics interferes and undermines their ability to reason for themselves.

Case in point: Negative attack ads work. Why? Because they cater to people's prejudices, hatreds and fears. Few voters stop to consider that if this guy is going after the OTHER guy, what does this guy actually offer HIMSELF, aside from being critical of their opponent? Poor reasoning skills presume that he offers the opposite of what he criticizes. Given the daily instances of blatant hypocrisy in politics these days, that's obviously an erroneous assumption.

Teaching route memorization accomplishes nothing without teaching critical thinking along side of it. If kids are memorizing a bunch of things, they're not taught to question them. Things like Jefferson being a slave owner and fathering kids with one of his slaves weren't taught in primary school when I was going. They should be, because it's our history and without questioning what's reported in our history, we'd never know these things and the one thing that history is supposed to teach us is some perspective on our world today and what NOT to do that went badly wrong back then.

Teach kids to think critically and the rest will follow. The owners of our country may not get the compliant, mindless drones they want to perpetually under-pay, but the quality of life for everyone else will only improve.

The idea of rote learning as a base upon which to build more complex thinking should be obvious. The kindest way I can put it is that Suzanne Kail must be binary-minded simpleton. Somewhere in the saga of epidemic stupidity, a few "educators" who fancy themselves all cutting-edge figured out what most of us already knew -- that learning doesn't end at memorization, and that higher levels of thought should indeed be encouraged. But in their tiny little either-or brains, there was no room for a complex layered viewpoint, so they jumped to the brick-headed conclusion of "memorization bad, exploration good, huhhhrrp derp." Education shouldn't even be an undergraduate field of study, it should be a very select graduate-level opportunity for those who have already proven themselves in another field, and then shown aptitude to lead students.

This article is still ridiculous: Murphy Paul acts like memorization is some kind of extinct skill: it is not. I will pay $1,000 to your favorite charity if you can find me a published curriculum that explicitly states that memorizing multiplication facts is unnecessary. So why should we care what Murphy Paul has to say when her ideas are so inane?

I think that people should “Drill” facts and things into kids minds, I think that it makes kids not want to learn to as much as they would of .I do think that we as students should learn by getting into our minds other than drilling it into our minds. I don’t think that learning cursive should be something mandatory that we need to learn like reading, but at the same time I don’t think that learning to type should overpower it. I am just wondering what makes people think that typing is more important than cursive, and if people know that writing improves thinking in reading and writing.

Instead of always advocating for one method over another, the smart teacher would use a balance on all methods in order to teach his/her students effectively. Instead of the either/or approach, it is better to use the both/and approach. Some students would do better with one method while other students would do better with another method. We all learn in various ways and each student has a preferred method. By using all methods in a blended fashion covers all students well. As a music teacher, I use so many different methods and styles that I am sure I have some in my tool box to help anyone who comes my way. You all know people or may even experienced this for yourself, that you began piano lessons (or whatever instrument) and for some reason along the way to Carnegie Hall, you concluded that music making was not possible for you, so you quit lessons and sold the instrument. As a music teacher, I put the blame on the music teacher for using only a singular method or a limit view of teaching music and the instrument. Music, like any subject is so multifaceted as are the students we teach that we need to have a vast array of methods and approaches to helping each student. Like doctors, we need to be able to diagnose the problem and prescribe a remedy other than "that two aspirin and see me in the morning". One size does not fit all!

I can certainly see some benefits to memorization. One benefit notmentioned here is in the art of studying to memorize information. Thestudy guides i have created to memorize have often helped me comprehend.I often find myself diagramming information to learn it. Withoutmemorization, our students may carry little information with them. Theyhave to rely solely on the information that is immediately available.Higher Levels of understanding can not be achieved with only using whatsimmediately available to you.

I made a simple argument recently that we should return to actively teaching Latin and Greek - from Kindergarten through at least 8th grade - why? Because most of math and science use Greek and Latin culture as at least some foundation or base. Additionally most math and science plus law either uses these languages directly or is heavily peppered with their constructs. And here's another plus: it would boost the test scores of kids whose native language might be - oh I don't know - Spanish? The response I was given from a parent whose child was from a bilingual household: my child doesn't need to learn another "foreign" language they have enough to learn already. If we start teaching foundation skills and building on them as we once did in our classrooms much of the rest will take care of itself. Learning a language isn't just about grammar - it's about culture - and it's about logic and reasoning and many other skills that cross-pollinate. It's a bit like saying music is an extra - music isn't an extra - teach a kid formal music theory and the joy of making music and you've built neural pathways, you've provided incredible opportunities for teaching applied physics, the musical notation has a direct transfer to mathematics and vice versa. I think we've gotten to the point where classical knowledge is somehow useless in post-industrial age. I would argue the opposite. I was sitting next to a colleague in an Adobe Flash class - she was a classically trained sculptor. She learned so many skills that transfer directly into her profession - she's a graphic designer. We underestimate the value of things that don't seem very relevant. We're so busy trying to create doctors and engineers that we don't want to give them the foundations that would help them to excel in those professions. What a loss.

I know some educators are philosophically opposed to memorizing, but I'm not one of them. There is certainly a place for it, particularly when the material to be memorized is fundamental, and instant recall of it provides some tangible benefit.

But in my personal and professional experience, memorizing roots doesn't meet that standard. I seldom rely on roots to figure out the meanings of words, and even when I occasionally do, it is the nth strategy I turn to. It usually isn’t worth the effort.

Once students get to something like the 3rd or 4th grade level, I find that the biggest issue impeding their fluency and their comprehension is frequent halts to puzzle out the meaning of unfamiliar words. When these interruptions are too frequent, they cause the reader to lose the overall sense of what is written. They are so wrapped up in figuring out the meanings of a few words, that they can no longer see the forest for the trees. After all, the point of reading is comprehension–vocabulary is merely a means to achieve comprehension.

Memorizing roots only gives readers who struggle in this way another opportunity for interruption and doesn't succeed often enough to provide a positive return on investment.

I don't see why cursive writing is beneficial. I am a TA for my colleges geology department, and the students who use cursive are frequently marked down when I grade their labs... not because they used cursive, but because their cursive handwriting is so sloppy that it is very difficult to read. She stated forming letters helps with fine motor skills, and that makes sense, but students can write letters without writing in cursive...

The million-dollar question...while we debate all the possible errors in this article, how many of our students would a) have the fortitude to read the whole article, b) evaluate the article based on its merits rather than blindly trusting the information presented, c) know how to fact check the article using reliable resources, and d) actually have the gumption to seek out the information to prove or disprove the article? I would argue very few. These are things we take for granted as educators that our students MUST LEARN. Perhaps we should spend less time talking about any possible errors in argumentation and offer our expertise in argumentation and evaluation to our students so they may model the same behavior!

This article is poorly researched, with over-broad conclusions for the very little research basis. Most of the positives are anecdotal, and not even worthy of writing up... "the kids were excited to use the roots... blah blah blah..." an effective teacher could get his or her kids excited to pick up cigarette butts and dog poop at the city park too, by making a fun game out of it, but that hardly means effective learning is happening.

In fact, one could make a great example of several argumentation/logical fallacies directly form this writing:

1. red herring. teaching good writing is not the same thing as teaching cursive, but the author makes that jump.

2. False choice: Either pro drill and kill, or never memorize math facts. There is a huge difference between memorizing the multiplication tables, and memorizing steps to solve more advanced math problems without understanding the thinking behind them.

3. Confusing anecdotes for evidence. So some teacher found that her students didn't mind memorizing... Does that prove they learned more? did they score better subsequently on tests of language? did they all go to college or something? It would be fairly trivial to find another calss that didn't like the memorization...[And as a personal note, I speak two romance languages just fine, and still don't know the latin roots... I also can't write in cursive to this day, didn't stop me from doing my graduate work at UC Berkeley]

Remind me NOT to buy her upcoming book, "brilliance: the science of smart."

Cursive is great if you need to write a note to yourself that you don't want your kids to read. That aside, the proliferation of computers has not resulted in American kids being more literate. I find now that many can barely spell or write. Educators should see the typing on the wall.

I want to preface this comment by stating that I am currently a first grade teacher- a friend linked this article to me via Facebook and I was annoyed enough to re-post my comment to her here. The title of the article is misleading. It implies that students should learn cursive, when in actual fact the article explained that the real skill they're talking about is handwriting. Cursive is often dropped in favor of typing because cursive was originally used to write faster. Now we have computers for that. Also, the fact that these kids are growing into a world that is dominated by technology means that it's more important for them to be more proficient typers than pretty writers. Handwriting, on the other hand, will never ever be taken out for all the reasons listed in the article and also common sense. I also found it interesting that the article focused on the research on handwriting and then slipped in the comment about Indiana no longer teaching cursive. They're not the same thing.Math facts: yes, it's important to memorize math facts so that you can remember them automatically. This is still taught in schools. We have a program called Reflex Math that is introduced late-1st grade where the kids play games that drill addition and subtraction facts (upper grades have multiplication and division). But drilling and killing math facts without understanding the logic that forms a basis for all mathematics means that those facts are all the students will ever know- yes, they can solve a math problem on a test, but they have no idea why they did what they did or what all those numbers mean. In the primary grades we form that basis by teaching the "21st-century skills" - problem solving, regrouping, defining numbers in terms of sets of ones/tens/hundreds, etc. Again, you need the latter to achieve the former.I have never heard of a teacher that DOESN'T read aloud to his/her students. It's still stressed as extremely important in every subject area. That's a far cry from "dying out."Sadly, it's these kind of fluff pieces that tend to fuel the ranting and raving of people who know little to nothing about education/teaching. I wish the author had done a little more research instead of citing outdated studies or blatant misinformation so that the general public wouldn't get confused.

To pile on a little further: why Latin and Greek roots? Unsurprisingly, the roots of most common English worlds are to be found in Old English, a dead language just like Latin and Greek, and many others are taken from French and are only distantly related to any Latin original. The difference is that Latin and Greek were part of the old-fashioned education for which Ms Murphy Paul is nostalgic, while Old English was not.

I was doubtful about the cursive claim and checked the link. The cited research is not about cursive It doesn't even support handwriting over typing. The actual claim is that *printing* letters is better than looking at them. I see that Kate Gladstone has spelt this point out in more detail below.

As a hint, teaching children argumentation by misleading quotation of sources worked pretty well in the days before the Internet. It's not such a good idea in the era of hyperlinks and Google

Yes, yes, there are a myriad number of ways to help children learn their computational facts; if we waved a magic wand over the entire US population and everyone knew their facts instantly, we'd still be at the bottom of the barrel in terms of mathematics achievement. Let's get real: it isn't lack of mastery in computational facts that is our problem: it has to do with our culture of learning, our all too short school year, our underfunded, crumbling schools, our undersupported and undervalued teachers, our poverty stricken and unhealthy children, our distracted parents, and oh so much more. As Nate Silver would say, you're all behaving like hedgehogs, when you should be thinking like foxes.

Jennifer, No one (certainly not me) is arguing that students should not learn facts. For example, I would be against students doing math with calculators (or some external memory device like a table) BEFORE they have acquired (internalized) math facts. However, that is not the same thing as saying the only way (or even the preferred way) to learn fractions or multiplication and division is through rote memorization(rehearsal). That is not to say that practice is not important. But practice to develop fluency may come later in the process AFTER the facts are meaningfully learned and require much less instructional time (particularly if appropriately spaced over time) than back to basic traditionalists would suggest.

I think Ms. Murhpy Paul has conflated rote memorization - which is an approach that relies on rehersal as a method of learning of information, with the importance of having accessible, retrievable knowledge in order to engage in higher order kinds of thinking like reading comprehension and math problem solving. I think most reform minded educators agree that knowledge is essential for thinking. The question is are there better ways of helping students acquire this foundational knowledge. The answer is yes! For example, we know that most children eventually become fluent in math facts WHEN they initially are encouraged to use strategies that make sense to them such as counting, derived fact strategies, etc. This happens because they are more likely to generate correct answers when using strategies, begin to make associations between answers and math fact problems, and eventually prefer to retrieve answers from memory (see Robert Siegler research on this for more info). The example regarding learning greek word roots seems to be an example not of rote memorizing but actually the opposite - teaching in meaning oriented ways that encourages students to use their knowledge to learn new information.

"The adoption of Alberta’s discovery math teaching techniques and curriculum has meant that in many Alberta elementary schools, teachers are discouraged from teaching the standard, time-honoured ways of long division and multiplication, vertical addition and subtraction, and the memorization of times tables."

You can send that $1,000 over to St. Jude Children's Research Hospital.

@DallinPaulJensen learning cursive means learning to write it well. those students are obviously poorly-trained in cursive and should be no sort of argument against the learning of cursive; rather, they should be an example of why we need to teach cursive even more extensively

@RobertoRibas What I found astonishing is that she has been given such a public platform to spout these ignorant and unoriginal ideas. Is Time so lacking of contributors that they would stoop to this level? Perhaps they'll go the way of Newsweek.

@sarahcatharina I agree - this article is very poorly researched, and many of the assertions show a complete ignorance of what is actually taking place in school. I attempted to contact Ms. Murphy Paul, and she refused to acknowledge my concerns to the point of blocking my emails asking which math curricula doesn't include knowledge of computational facts.

@john.quiggin It appears that many of the studies that Ms. Murphy Paul uses to support her ideas is either out of date, or irrelevant. It was the same thing with her quote that lack of mastery of computational facts prevented access to higher math. I wonder if her entire book is going to be this sloppy?

"...that is not the same thing as saying the only way (or even the preferred
way) to learn fractions or multiplication and division is through rote
memorization(rehearsal)"

Please inform me, then: how WOULD one memorize one's multiplication tables (or one's ABCs, or how to play the flute, or how to program in C++) without simply doing the process over and over again? I'm not saying memorizing facts is the ONLY thing important in learning. It's surely not. I'm just saying it's necessary to memorize the basics before one can solve practical math problems (or write a novel, or play in a chamber orchestra, or solve a scientific problem).

@EDPSYCH Have you ever tried to teach a middle or high schooler algebra, when she's really struggling? And not just on a single lesson, but on ALL of algebra, I mean. I can almost guarantee that the reason she's struggling at algebra is because she doesn't understand fractions. And the reason she doesn't understand fractions is usually because she never memorized her basic multiplication and division tables, and thus can't DO the fractions at all quickly.Sorry, but I don't agree. A student with a multiplication table in front of him might be able to do multiplication, but they're still likely to struggle with fractions and, later, algebra. Some things you need to internalize in order to use well.

rmberkman: Instead of writing endless posts attacking the writer here, why not invest that time and energy into writing a coherent paper espousing your own point of view on this topic? As far as studying root meanings of words is concerned, its value is a simple matter of practical application and observable results. Learning about root meanings of words gives kids a sense of the almost architectural nature of grammatical construction, its correlation to human thought processes, and its almost inexhaustable flexibility and beauty.

@rmberkman@john.quiggin Is that a biasless fact or an opinion? If it is an opinion, perhaps it is out of date too... where does that put the truth? Lets break this down into motives... What's her motive? What's yours? How does your motives affect your actions?

Are you are arguing against the necessity of the just plain hard work of repetition and memorization in grammatical learning? If so, you do a disservice to teachers and students who need a good stiff dose of reality on this topic.

@JenniferBonin@dagelf@john.quiggin because learning a language by being able to tell the difference between words is utterly useless? there's thousands of english words out there-how are we supposed to go through each and "make clear the similarities" between all of them? If, for instance, some kid was reading a book and came across the unfamiliar word "homeostasis", how would he/she figure out what it means? by trying to identify other words that look "similar" to it? absolutely not! a student well versed in latin/greek roots will find out that homeo means unchanging and stasis means equilibrium, and thus can guess that "homeostasis" means maintaining equilibrium.

and 29% of all english words come from latin, and almost no words remain from celtic, if thats the "old english" that you mean

@dagelf@rmberkman@john.quiggin I'm an economist, not a teacher and my kids are long past learning to write. I don't have any motive at all, except for the xkcd problem of wanting do something when "someone on the Internet is wrong" -

I was surprised by what was asserted in the article, checked the supporting evidence and found that it had been misdescribed.

@dagelf@rmberkman@john.quiggin I'm not clear what you're asserting here. We were pointing out that the "research" cited in the article does not suport the contentions. It is not a matter of opinion; it is fact. Check into the research yourself and form your own opinion. I'm certain you'll agree.

@JenniferBonin Sigh so much of what we teach to the young is not understood until we are older (and, presumably, wiser.) I'm 53 years old, have been teaching fractions for the past 30 years, and I still don't understand everything there is to know about them.....

...Actually, even today, I visualize (1/4 x 7/8) as one quarter of 7/8. That is, if I had a picture of 7/8's of a pie, (1/4x7/8) is a quarter the size of that. Which IS pretty much repeated addition, in an inverse sense: I need (4/1 = 4) sets of (1/4 x7/8) in order to get my original 7/8. It's really the same sort of logic as explaining 4x5, once you understand what an inverse/reciprocal means.For the record, I've seen fractions in such a light since my fourth grade teacher first drew pictures explaining why 6 divided by 1/2 was 12, not 3. So it's not just the engineering degree that gave me the insight, though I'm sure I can explain it better now than I could at age 9.

You ignore the obvious fact that writing skills have declined in the U.S. Having graded freshman papers, I have first hand experience with this. Show me the school where the kids are learning the nuts and bolts of grammar. They are not, in all too many cases. Therefore, the study of root meanings is a step in the right direction, language skills wise.

@EDPSYCH@JenniferBonin What's so funny is how many teachers know how to multiply, but don't know much ABOUT multiplication. For example, if you asked them to explain it, they would say "well, it's repeated addition." But that only covers multiplication by a whole number (4 x 5, etc.) How do you explain what multiplication is when you have 1/4 x 7/8? People like Ms. Murphy Paul believe that knowing multiplication facts implies knowing multiplication; nothing can be further from the truth.

@JenniferBonin@EDPSYCH Again, I agree that being able to quickly retrieve a basic math fact (addition, multiplication, etc) from memory is important. We also seem to agree that it is important that students understanding the meaning of multiplication and be able use multiplication facts in problem solving. We even agree that practice retrieving math facts so that fluency develops is important. So it seems like our only point of disagreement is the relative emphasis and balance of these instructional components. And of course the balance will depend somewhat on the students, what the prior instructional experiences were like, etc. I tried to give a sense of what a "strategies first" approach might look like for addition and subtraction; multiplication is a bit more involved but here are some references for you to check out so you can begin to get a sense of what this might look like in practice and some of the research support for this approach:

@JenniferBonin@EDPSYCH Nobody's arguing about the importance of memorizing multiplication tables. Murphy Paul is simply making a big deal about something that was settled a long time ago. Perhaps she has nothing relevant to write about, so she picked this topic.

@JenniferBonin@rmberkman@EDPSYCH I think we're all preaching to the choir here; the fact is that Murphy Paul is stating that we should "go back to" memorizing multiplication facts. The problem is this: we never left! I've been teaching for the better part of 30 years, and every school I've ever worked in and every teacher I've ever met has taught multiplication facts. Why is Murphy Paul advocating something that is already being done? It just seems like her ideas are irrelevant and unimportant.

@rmberkman@EDPSYCH@JenniferBonin I completely agree that memorizing facts isn't enough. Along with it, we need to teach WHY those facts are what they are (ie: what does multiplication MEAN?), and also how to use those facts in real life (ie: problem solving). As an engineer, I surely won't argue against that!But my point is that you can't solve problems, no matter how clever you are, without the right tools. Memorized basic principles are a tool. And knowing that 5x2 is like the number of blocks in an area five columns wide and two columns high doesn't typically help if you can't actually figure out what 5x2 equates to.

@EDPSYCH@JenniferBonin Feel free to demonstrate to me how, precisely, one learns her multiplication tables EXCEPT through some form of rote memorization. A good teacher (or parent) will try to switch up the form that memorization takes, so it's not quite so mind-numbing -- like alternatively using flashcards, minute quizzes, verbal competitive games between students, etc. But when you come right down to it, in order to move forward to more interesting math, a student simply MUST have her multiplication tables memorized.As I said, I've actually tutored kids who struggled with multiplication. I have never ONCE seen a kid "develop fluency ... later in the process AFTER the facts are meaningfully learned". Never. What I've seen instead, many times over, is that a kid who isn't comfortable with multiplication and can't do most problems reasonably quickly tries to learn division, and struggles. And then she tries to lean fractions, and everything falls apart. Because in order to solve 5/3 + 1/12, you MUST be able to recognize that 3*4 = 12 and 1*12 = 12. And you need to be able to do it in your head, without spending a lot of time sorting things out. If you can't, then there's just no way you can solve the problem quickly enough to finish a whole set of them on a test. And when the problems get harder (ie: division of fractions), the situation just gets worse. Once kids are in over their heads, they don't typically go back to practice their multiplication tables. They should, but they don't. Usually they don't really realize that that's at the root of the problem -- it's hard to see what the problem is, if you don't understand what's going on, after all. So, sorry, but I've got to disagree. If you want a kid to do decent at math in middle/high school, you've got to be sure they really memorize the basics back in elementary school.

@EDPSYCH@JenniferBonin I don't remember a time when kids were >not< required to memorize facts. The only time I remember was when it was downplayed to include problem solving, which is a much more important math skill.

@JenniferBonin Jennifer, No one (certainly not me) is arguing that students should not learn facts. For example, I would be against students doing math with calculators (or some external memory device like a table) BEFORE they have acquired (internalized) math facts. However, that is not the same thing as saying the only way (or even the preferred way) to learn fractions or multiplication and division is through rote memorization(rehearsal). That is not to say that practice is not important. But practice to develop fluency may come later in the process AFTER the facts are meaningfully learned and require much less instructional time (particularly if appropriately spaced over time) than back to basic traditionalists would suggest.Read more: http://ideas.time.com/2012/11/08/why-kids-should-learn-cu-cursive/#ixzz2BkdoIjtn